A store increased the price of a bicycle by 25%. Later, the... | SAT Percentages Question, Answer Explained

Math · Problem-Solving and Data AnalysisMedium

A store increased the price of a bicycle by $25\%$ . Later, the store decreased the new price by $20\%$ . The final price is what percent of the original price?

$80\%$

$100\%$

$105\%$

$125\%$

Show answer and explanation

Answer: B

Increasing a price by $25\%$ multiplies it by $1.25$ , and decreasing the new price by $20\%$ multiplies it by $0.80$ . Overall, the original price is multiplied by $1.25 \times 0.80 = 1$ , so the final price is $100\%$ of the original price.

Choice C combines the percents as $25 - 20 = 5$ , but the $20\%$ decrease is taken from a larger price, so it removes as many dollars as the increase added.

Why the other choices are wrong

A. 80% reflects only the 20% decrease and ignores the earlier 25% increase.
C. This combines the percents as 25 minus 20. The 20% is taken from a larger price, so the changes cancel.
D. 125% reflects only the 25% increase and ignores the later 20% decrease.

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